Bugs Bunny was $42$ meters below ground, digging his way toward Albuquerque, when he realized he wanted to be above ground. He turned and dug through the dirt diagonally for $100$ meters until he was above ground. What is the angle of elevation, in degrees, of Bugs Bunny's climb? Round your final answer to the nearest tenth.
Answer: The strategy Model the situation as a right triangle. Determine the appropriate trigonometric ratio in order to find the missing angle. Form an equation and solve for the missing angle. Calculate the final result and round. Modeling as a right triangle This situation can be modeled by the following right triangle. The hypotenuse is $100\text{ m}$ and the height is $42\text{ m}$. We are asked to find the angle of elevation, which is the angle on the left. $?$ $100$ $42$ Determining the appropriate trigonometric ratio We are given the side ${\text{opposite}}$ to the missing angle and the $C{\text{hypotenuse}}$. The appropriate trigonometric ratio is therefore the $\text{sine}$. Forming an equation and solving Denoting the missing angle by $\theta$, we obtain the equation $\sin(\theta)=\dfrac{42}{100}$. Solving the equation, we get $\theta=\sin^{-1}\left(\dfrac{42}{100}\right)$. Evaluating this result in the calculator and rounding to the nearest tenth, we get $\theta=24.8^\circ$. Summary The angle of elevation of Bugs Bunny's climb is $24.8^\circ$.